Problem: Jessica is 4 times as old as Daniel. Twelve years ago, Jessica was 7 times as old as Daniel. How old is Jessica now?
Explanation: We can use the given information to write down two equations that describe the ages of Jessica and Daniel. Let Jessica's current age be $j$ and Daniel's current age be $d$ The information in the first sentence can be expressed in the following equation: $j = 4d$ Twelve years ago, Jessica was $j - 12$ years old, and Daniel was $d - 12$ years old. The information in the second sentence can be expressed in the following equation: $j - 12 = 7(d - 12)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $j$ , it might be easiest to solve our first equation for $d$ and substitute it into our second equation. Solving our first equation for $d$ , we get: $d = j / 4$ . Substituting this into our second equation, we get: $j - 12 = 7($ $(j / 4)$ $- 12)$ which combines the information about $j$ from both of our original equations. Simplifying the right side of this equation, we get: $j - 12 = \dfrac{7}{4} j - 84$ Solving for $j$ , we get: $\dfrac{3}{4} j = 72$ $j = \dfrac{4}{3} \cdot 72 = 96$.